I found the last proof of there being a prime divisor congruent to 1 mod m of m^m - 1 to be a little confusing. It might take a bit to digest that one. Just trying to follow all of the logic was tough for me. I am not quite sure why they were taking products of m/primes and so forth. I might just have to look at it again.
However, the others proofs of proving that various congruences had infinitely many primes in them was also exciting. I found it interesting that with the same modulus, the variety of methods used to prove the different equivelances to be impressive. It was interesting that one size did not fit all.
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